物理化学英文1气体状态方程 The Properties of Gases Equations of State

Bigelow, 1912
The Properties of Gases Equations of State
Bulk Variables
Volume - m3 Pressure - Pa Temperature - K Composition - moles
length3
Volume
units
Ideal Gas Law
pV nRT
p = pressure V = volume n = moles T = temperature R = universal gas contant = 0.08206 L-atm/mol-K
Partial Pressure
pAV nART
pA = partial pressure of gas A V = total volume nA = moles of gas A T = temperature R = universal gas contant = 0.08206 L-atm/mol-K
-2
attractive
-3
1.5
2.0
2.5
3.0
3.5
4.0
distance
Taylor Series
f(
x)
=
f(
0)
+
f
(0)x
+
1 2
f
(0)x2
where f (0) = df dx
and
x0
f (0)
=
d2 f dx 2
x0
Taylor Series Example
f(x) 1 f(0) 1 1 x
Compressibility
The compressibility of a gas is defined by
Z pVm RT
• If the gas behaves ideally, then Z=1 at all pressures and temperatures.
• For real gases, however, Z varies with pressure, and deviates from its ideal value
Virial Expansion
Z( p) Z(0) Bp Cp2
pVm RT 1 Bp Cp2
where B second virial coefficient C third virial coefficient
Virial Expansion
Z (1/Vm ) Z (0) B(1/Vm ) C(1/Vm )2
p V T c (atm)
m,c (cm3)
c (K)
He 2.26 57.76 5.2
Ar 48.00 75.25 150.7
N2 33.54
90.10 126.3
O2 50.14
78.00 154.8
CO2 72.85
94.0 304.2
Inflection Points
1500
y (x)
1000
m3 or cm3
1m
liter = 1000 cm3
molar volume Vm= V/n
1m 1m
Force/Area
Pressure
units
Pascal = Newton/m2 = Joule/m3
h
atmosphere = 101325 Pa
bar = 100000 Pa
mm Hg
torr
Physical Chemistry
Definition of Physical Chemistry
Physical chemistry stands in the same relation to the subdivisions of chemistry in which philosophy stands toward all the sciences. Its main object is to unify thought within the science of chemistry; therefore, it might well be named, the “philosophy of chemistry” - S.L.
Z
Argon Compressibility
2.5
2.0
Z = pVm/RT
1.5
1.0
attractive
0.5
0.0
0
200
400
600
pressure (atm)
273 K
repulsive
800
1000
Intermolecular Forces
4
3
2
Energy
1
0
-1
repulsive
Temperature
thermometry T ~ Volume
only for an ideal gas
or real gases in the low pressure limit
Composition
moles: ni S ni = n
mole fraction: xi S xi = 1
150
4000K
100
2000K
50
1000K
500K
100K
0
0.0
1.0
2.0
3.0
4.0
5.0
Vm/L
van der Waals Isotherms - Ar
200
500K
150
200K
100
150K5001Fra bibliotek0K-50
-100
0.00
0.10
0.20
0.30
0.40
Vm/L
Critical Constants
f (x)
1
1 x
2
f (0)
1
f (x)
2
1 x3
f (0)
2
1 1 x x2 x3 1- x
Convergence of (1-x)-1
x 1+x 1+x+x2 1+x+x2+x3 (1-x)-1 0.01 1.010 1.010 1.010 1.010 0.10 1.100 1.110 1.111 1.111 0.20 1.200 1.240 1.248 1.250 0.30 1.300 1.390 1.417 1.429
van der Waals Virial Expansion
1 Vm
b
1 Vm
1
b Vm
b2 Vm2
p
RT Vm
1
b
a/ Vm
RT
b2 Vm2
500
y'
0
y"
-500
-10
-5
0
5
10
x
Inflection Points
At the inflection point x0
dy 0 dx xx0
and
d2y dx 2 xx0
0
Carbon Dioxide Critical Isotherm
600 500 400 300 200 100
Use an intial estimate to evaluate the right hand side.
Use this calculated value of V as a better estimate.
Repeat till converged.
Ideal Gas Isotherms
200
Advantages fits gas data as accurately as desired. uses the ideal gas law as a base.
Disadvantages infinite number of terms. virial coefficients are temperature dependent.
0 0.0
304 K
Ideal Gas Real Gas
0.1
0.2
0.3
0.4
Vm /L
van der Waals Inflection Point
dp dVm
RT (Vm b)2
2a Vm3
0
d2p dVm2
2RT (Vm b)3
6a Vm4
0
solution: Vm,c 3b and pc a / 27b2
van der Waals Equation
p a / Vm2 Vm b nRT
repulsion
Vm,eff Vm b
peff p a / Vm2
attraction
van der Waals Equation
p
RT Vm
b
a Vm2
van der Waals constants
pVm RT 1 B /Vm C /Vm2
where B = second virial coefficien t C = third virial coefficien t
Relation of p and 1/V Expansions
B B RT
C
C B2
RT 2
Second Virial Coefficients B
100 K 273 K 373 K 600 K
He
11.4 12.0 11.3 10.4
Ar -187.0 -21.7 -4.2 11.9